SATURDAY, March 29, 2025, Purdue University, WEST LAFAYETTE, IN
Funding is available to cover accommodations for some participants.
Fill out the form here to register and/or apply for lodging support.
The deadline (March 8) to apply for lodging support has passed.
Speakers:
Nir Avni (Northwestern)
Aaron Calderon (UChicago)
Jonah Gaster (UW-Milwaukee)
Nimish Shah (OSU)
Schedule:
Times below are given in Eastern Time.
10:00-10:30 Registration and Refreshments
10:30-11:20 Aaron Calderon
11:30-11:45 Coffee Break
11:45-12:35 Nimish Shah
12:45-2:30 Lunch Break
2:30-3:20 Jonah Gaster
3:30-4:00 Coffee Break
4:00-4:50 Nir Avni
5:00 Farewells
Parking and Local Info:
Parking is free over the weekend and after 5pm on weekdays at the University Street Parking Garage, 201 N University St.
(no overnight parking)
All activities will take place in the Math Science Building, 150 N University St.
Talks are in Math 175 (use the north entrances of the building).
Registration and Refreshments are right outside Math 175.
Food:
Chauncey area (near campus, 10-15 min walk):
Maru (sushi, lunch box), String Ramen (Japanese), Poke & Hibachi, Noodles & I (Chinese noodles), YGF Malatang, Eight-Eleven Bistro (multi-cuisine), Garbanzo (Mediterranean), Chipotle (Mexican), Fiesta Mexican Grill, Pizza Uncommon, Raising Cane’s Chicken fingers, Triple XXX (burger), Taste of India, Jimmy John's, Potbelly.
Other places near campus:
Another Broken Egg Cafe (brunch), Ohana (poke).
Wabash landing (7 min drive):
Panera (salads, sandwiches), Adda Indian, Peppercorns (Chinese), Taste (Chinese).
Lafayette downtown (8-10 min drive):
BRU Burger (burger, salad), Yatagarasu (Japanese ramen), RedSeven (American), Bistro 501 (French), Black Sparrow (pub, dinner only for Saturday), La Scala (Italian, dinner only).
[There are other good restaurants not listed here.]
Coffee and Tea:
Greyhouse Coffee (one on campus and another in Chauncey), Vienna Espresso, Leaps Coffee, Tsaocaa (朝茶, bubble tea).
Organizers:
Lvzhou Chen (Purdue)
Marlies Gerber (IUB)
Bogdan Nica (IUI)
Nick Salter (Notre Dame)
Support:
This GGD workshop is funded with the support of the Purdue Department of Mathematics, IU Mathematics Journal, and the National Science Foundation.
Titles and Abstracts
Nir Avni
Title: Conjugacy width of higher rank arithmetic groups
Abstract: The width of a subset X of a group G is the diameter of the connected components of the Cayley graph of (G,X). This talk will be about width in arithmetic groups. For many natural classes of subsets (e.g. conjugacy classes, verbal sets, the set of unipotents) there is a conjectural dichotomy between rank 1 groups (where width is infinite) and higher rank groups (where, conjecturally, width is finite). I will present several partial results and talk about their applications, mainly to the model theory of higher rank groups, their Ulam stability, and classification conjugation invariant norms in them. This is a joint work with Chen Meiri.
Aaron Calderon
Title: The shape of best-Lipschitz maps between hyperbolic surfaces
Abstract: A common theme in geometry is that to study an object, you should study its moduli space. In the 80s, Thurston proposed a new metric on the moduli space of hyperbolic surfaces that measures the Lipschitz distortion between two metrics and whose structure connects to the geometry of curves on surfaces. Geodesics in this metric are not unique, and despite recent advances relating them to limits of harmonic maps, they remain hard to describe explicitly. In this talk, I’ll discuss recent progress in understanding what these geodesics “look like.” This represents joint work with Jing Tao.
Jonah Gaster
Title: Hyperbolic geometry and the Markov Unicity Conjecture
Abstract: The Markov Unicity Conjecture asserts that there are no unexpected coincidences in the simple length spectrum of the “modular torus” (that is, the quotient of the hyperbolic plane by the commutator subgroup of the modular group): two simple closed geodesics of equal length should differ by an isometry of the surface. I will give a quick intro to this problem, discuss some things that can be made transparent from the viewpoint of hyperbolic geometry, and indicate some open avenues for future research.
Nimish Shah
Title: Limiting distributions of o-minimal curves on homogeneous spaces
Abstract: We show that the image of any trajectory in SL(n,R) whose co-ordinate functions are definable in an o-minimal structure; for example, rational functions, on the quotient space SL(n,R)/SL(n,Z) get equistributed with respect to an algebraically defined measure, provided that the trajectory does not contract a pure tensor to 0 in any exterior representation of SL(n,R). We will also give some interesting new examples of such curves that equidistribute in the whole space. This is a joint work with Michael Bersudsky and Hao Xing, and extends earlier work of Shah for polynomial trajectories.